Quantum Interference In Spontaneous Emission And Probe Absorption Of An Atom Embedded In Double-Band Photonic Crystal

The main purpose of this thesis is to investigate the quantum interference effects in an atom, which is embedded in Double-Band Photonic Crystal. The systems we considered include a three-level coupled by a strong coherent field and a double-V type four-level atom. This thesis is consisted of three parts as the follows.â… . Spontaneous Emission spectrum of a Three-Level Atom Embedden in Photonic CrystalIn this part, wo study the spontaneous emission spectrum and quantum interference of a three-level atom coupled by a strong coherent field, which is embendded in double-band photonic crystal,as shown in Fig. 1. S. Y. Zhu has study the same model in free-space vacuum reservoir. Here, we assume the atom is embendded in isotropic Photonic Crystal reservoir, so that the spontaneous emissionω_k from the upper level |2> to the lower level |1> is coupled by the isotropic PC reservoir. The transition from |3> to |2> is coupled by laser coherent field eω₀. We can get the figure of spontaneous emission spectrum as the function of detuningδ_k as shown in Fig. 2.It is shown that, in Fig. 2. a, the result is as the same as Zhu's. It is can be explained by dressed states. Well, in Fig. 2. b, because of the photonic band gap there is depressed emissions in the spontaneous emission spectrum.When the detuning of strong coherent field does not equal zero, we get the Fig. 3. The result is similar to Zhu. We get the same result as Zhu did as shown in Fig. 3.a. In Fig. 3. b, there is depressed emissions in the spontaneous emission spectrum, too. So, we can see that using our new-method to solve the spontaneous emission spectrum of this three-level atom, we will get the same result as others in free-space vacuum reservoir. In the Photonic Crystal reservoir, the photonic band gap will reduce depressed emissions in the spectrum.â…¡. Quantum interference Effects on the Spontaneous Emission of a Four-Level Atom Embendded in Photonic CrystalIn this part, the model of a four-level atom embedded in a double-band photonic crystal isadopted. Consider a four-level atom with upper levels |3> and |2>, and lower levels |1> and |0> as shown in Fig. 4. We assume that the transitions from the two upper levels to the lower levels are coupled by the same reservoir which is respectively isotropic PC modes, anisotropic PC modes and free vacuum modes. 1. Effect of split ground state levels on the spontaneous emission spectrumWe first investigate the effect of the splitting on the spontaneous emission spectrum in the PC and free vacuum reservoirs. We plot the spontaneous emission spectrum as a function of detuning for different splitting widths of the ground state levels as shown in Fig. 5. From the Fig. 5 (b) and (c), we see that the spontaneous emission peaks correspond to the resonant transitions from the upper two levels to the lower two levels. This is expected and understandable as the splitting changes the resonant positions of the atomic transitions in both cases of the anisotropic PC and free vacuum reservoirs. However, for the case of isotropic PC reservoir (Fig. 5(a)), the effect of the splitting width A on the spontaneous emission spectrum is quite different. It is seen that additional and unexpected peaks appear besides the. peaks corresponding to the resonant transitions from the upper levels to the lower levels.We find that the peaks resulting from the splitting of the atomic ground state stem from the contribution of the splitting to the Laplace transform of the delayed Green's function of the isotropic PC modes. Physically, the characteristic of isotropic photonic crystal leads to this optical singularity. The atom exchanges energy back and forth with its own radiation, backscattered after tunneling a localized distance. The atomic level splits into dressed states caused by the strong interaction between the atom and its own radiation. And then new spontaneous emission spectrum peaks come into being. Besides the inhibition of light wave propagation in photonic crystal makes the spectrum cancellation in Fig. 5, the new additional narrow peaks are very important and more useful in spectrum analysis, quantum computer, optical switch and so on. Yet, the potential use needs much more work because the phenomena only occur in the isotropic DOS model, which has an unphysical van Hove singularity at the band edge but not present in any realizable 3D system.2. Quantum interference in spontaneous emission spectrumIn order to the investigate quantum interference in this system, we study first the case that an atom is equally and synchronously pumped to the upper levels, employing symmetric values of parameters for the four transitions. In Figs. 6 (a), (b) and (c), the spontaneous emission spectra are shown for the cases of isotropic PC reservoir, anisotropic PC reservoir, and free-space vacuum reservoir, respectively. While quantum interference is seen to have weaker effect on the spontaneous emission spectrum in the cases of isotropic and anisotropic PC reservoirs, it leads to two depressed emissions in the spectrum in the case of free-space vacuum reservoir. We consider next case when an atom is assumed to be initially pumped to level |3〉with asymmetric parameters for four atomic transitions. The ensuing emissions are seen to present a different picture with prominent features as shown in Fig. 7. The quantum interference jointly induce two narrow spectral lines, position near the transitions frequencies from the empty upper level |2〉to lower levels |0〉and|1〉. This can be understood as the spectrum induced by transitions of population from the upper two levels to the lower levels and by emission interference accompanying with these transitions. Therefore, the quantum interference induce a population transfer from level |3〉to empty level |2〉while the emission interference of population from upper levels to the lower levels isdestructive. Hence, the narrow spectral lines are seen to arise from a p opulation transfer under destructive emission interference.â…¢. Quantum interference Effects on the Spontaneous Emission of a Four-Level Atom Embendded in Photonic CrystalIn this part, we consider a doubleâ…¤-type four-level atom with upper levels |3〉and |2〉, and lower levels |1〉and |0〉. We assume that the transitions from the two upper levels to |0〉are coupled by the isotropic (anisotropic) double-band PBG modes or vacuum modes(ω_k), and the transitions to |1〉which are far away from the gap, synchronously coupled by the free vacuum modes(ω_λ) and a weak probe field (ω_p) as shown in Fig. 8. We firstly study the case using symmetric values of parameters. In Fig. 9 (a), the two peaks correspond to the transitions of an atom from two upper levels |3〉and|2〉 to the lower level |1〉. Whereas, in Fig". 9 (c), the two" transitions from upper levels to level |1〉merge into only one peak because of narrow width of the two upper levels. There are three transparencies in the case of isotropic PBG reservoir (Fig. 9(a)), but only one transparency in the case of anisotropic PBG (Fig. 9(b)) and free vacuum reservoir (Fig. 9(c)). The transparency at the center ofδ_p= 0 in all the three cases is similar to that reported by Zhou and has been attributed to the two types of quantum interference that exist simultaneously in the system. It is further seen that the two transparencies at symmetric locations ofδ_p = 0 in Fig. 9(a) result from the density of state (DOS) of the isotropic PBG modes. It is also clear that the interference effects on probe absorption spectrum in the case of the isotropic PBG or anisotropic PBG reservoir is weaker than that in the case of free-space vacuum reservoir.However, the situation is quite different from above if the asymmetric parameters of the system are employed. Fig. 10. Figs. 10 (b) and (c) show the behaviors of the probe absorption spectra in the cases of anisotropic PBG reservoir and free-space vacuum reservoir. While there is a certain degree of similarity to that shown in Fig. 9, the symmetry of the spectrum is completely removed. Fig. 10 (a) shows new features of an additional transparency and the elimination of a probe absorption spectral line in the case of the isotropic PBG reservoir. The symmetric transparencies in Fig. 10 (a) still result from the twosingularities in the Laplace transform of the delayed Green's function. Whereas, the additional transparency and. spectral line elimination in Fig. 10 (a) is the consequence of destructive interference of the doubleâ…¤-type transitions.The probe absorption elimination discussed above are calculated with simultaneous presence of both types of quantum interference arising from the transitions between the two upper levels to |1〉and|0〉. we consider the absorption and dispersion spectra with different coherent coupling constants as shown in Fig.11 for the isotropic PBG reservoirs. We can see that the probe absorption line elimination in the case of isotropic PBG reservoir is mainly the result of the interference between the transitions from the two upper levels to|0〉, and the additional transparency in the case of isbtropic PBG reservoir stem from the combination of the two types of interference.So far, we studied the quantum interference effects in an atom, which is embedded in Double-Band Photonic Crystal. The conclusion and new phenomena are very important and more useful in spectrum analysis, quantum computer, optical switch and so on.